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In the present paper, the dynamic response of a nonlinear plate embedded into a fractional derivative viscoelastic medium is studied by the method of multiple time scales under the condition of the combinational internal resonances of difference type using a newly developed approach resulting in uncoupling the linear parts of equations of motion of the plate. The influence of viscosity on the energy exchange mechanism between interacting nonlinear modes has been analyzed

Fractional Calculus Application in Problems of Non-linear Vibrations of Thin Plates with Combinational Internal Resonances